Superluminal advanced transmission ofXwaves undergoing frustrated total internal reflection: The evanescent fields and the Goos-Hänchen effect

A study of X waves undergoing frustrated total internal reflection at a planar slab is provided. This is achieved by choosing the spectral plane wave components of the incident X wave to fall on the upper interface at angles greater than the critical angle. Thus, evanescent fields are generated in the slab and the peak of the field tunneling through the slab appears to be transmitted at a superluminal speed. Furthermore, it is shown that for deep barrier penetration, the peak of the transmitted field emerges from the rear interface of the slab before the incident peak reaches the front interface. To understand this advanced transmission of the peak of the pulse, a detailed study of the behavior of the evanescent fields in the barrier region is undertaken. The difference in tunneling behavior between deep and shallow barrier penetrations is shown to be influenced by the sense of the Goos-Hänchen shift.